Quantum Mechanics: Theory and Applications

1. Front Matter

   Pages i-xlviii

   PDF

2. Mathematical Preliminaries

   1. Front Matter

      Pages 1-1

      PDF

   2. The Dirac Delta Function

      • Ajoy Ghatak, S. Lokanathan

      Pages 3-18

   3. Fourier Transforms

      • Ajoy Ghatak, S. Lokanathan

      Pages 19-27

3. Basic Quantum Mechanics

   1. Front Matter

      Pages 29-29

      PDF

   2. Particles and Waves and the Uncertainty Principle

      • Ajoy Ghatak, S. Lokanathan

      Pages 31-70

   3. Time Dependent Schrödinger Equation

      • Ajoy Ghatak, S. Lokanathan

      Pages 71-88

   4. Propagation of Wave Packets and Concept of Group Velocity

      • Ajoy Ghatak, S. Lokanathan

      Pages 89-114

   5. Bound State Solutions of the Schrödinger Equation

      • Ajoy Ghatak, S. Lokanathan

      Pages 115-158

   6. Linear Harmonic Oscillator: I Solution of the Schrödinger Equation and Relationship with the Classical Oscillator

      • Ajoy Ghatak, S. Lokanathan

      Pages 159-196

   7. One-Dimensional Barrier Transmission Problems

      • Ajoy Ghatak, S. Lokanathan

      Pages 197-220

   8. Angular Momentum I—The Spherical Harmonics

      • Ajoy Ghatak, S. Lokanathan

      Pages 221-244

   9. Spherically Symmetric Potentials Hydrogen Atom Problem, Rotation Vibration Spectra, Three-Dimensional Oscillator

      • Ajoy Ghatak, S. Lokanathan

      Pages 245-290

   10. Dirac’s Bra and Ket Algebra

       • Ajoy Ghatak, S. Lokanathan

       Pages 291-307

   11. Linear Harmonic Oscillator II Solutions Using Bra and Ket Algebra

       • Ajoy Ghatak, S. Lokanathan

       Pages 308-338

   12. Angular Momentum II Using Bra and Ket Algebra

       • Ajoy Ghatak, S. Lokanathan

       Pages 339-356

   13. Experiments with Spin Half Particles The Stern-Gerlach Experiment, Larmor Precession and Magnetic Resonance

       • Ajoy Ghatak, S. Lokanathan

       Pages 357-388

   14. Angular momentum III Eigenfunctions Using Operator Algebra

       • Ajoy Ghatak, S. Lokanathan

       Pages 389-400

   15. The Double Well Potential and the Krönig-Penney Model

       • Ajoy Ghatak, S. Lokanathan

       Pages 401-422

   16. The JWKB Approximation

       • Ajoy Ghatak, S. Lokanathan

       Pages 423-477

An understanding of quantum mechanics is vital to all students of physics, chemistry and electrical engineering, but requires a lot of mathematical concepts, the details of which are given with great clarity in this book. Various concepts have been derived from first principles, so it can also be used for self-study. The chapters on the JWKB approximation, time-independent perturbation theory and effects of magnetic field stand out for their clarity and easy-to-understand mathematics. Two complete chapters on the linear harmonic oscillator provide a very detailed discussion of one of the most fundamental problems in quantum mechanics. Operator algebra is used to show the ease with which one can calculate the harmonic oscillator wave functions and study the evolution of the coherent state. Similarly, three chapters on angular momentum give a detailed account of this important problem. Perhaps the most attractive feature of the book is the excellent balance between theory and applications and the large number of applications in such diverse areas as astrophysics, nuclear physics, atomic and molecular spectroscopy, solid-state physics, and quantum well structures.

• Angular Momentum
• Dirac Delta Function
• Dirac's Bra and Ket Algebra
• Schrödinger Equation
• The JWKB Approxiamtion
• quantum mechanics

• Indian Institute of Technology, New Delhi, India

  Ajoy Ghatak

• Jawahar Lal Nehru Planetarium, Bangalore, India

  S. Lokanathan

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